What is (\partial)/(\partial x)(3x^2-6xy+y^3-9y+5) ?

The answer to (\partial)/(\partial x)(3x^2-6xy+y^3-9y+5) is 6x-6y

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(\partial)/(\partial x)(3x^2-6xy+y^3-9y+5)

\frac{\partial}{\partial x} (3 x^{2} - 6 x y + y^{3} - 9 y + 5)

6 x - 6 y

Solution steps

\frac{\partial}{\partial x} (3 x^{2} - 6 x y + y^{3} - 9 y + 5)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (3 x^{2}) - \frac{\partial}{\partial x} (6 x y) + \frac{\partial}{\partial x} (y^{3}) - \frac{\partial}{\partial x} (9 y) + \frac{\partial}{\partial x} (5)

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

\frac{\partial}{\partial x} (6 x y) = 6 y

\frac{\partial}{\partial x} (y^{3}) = 0

\frac{\partial}{\partial x} (9 y) = 0

\frac{\partial}{\partial x} (5) = 0

= 6 x - 6 y + 0 - 0 + 0

Simplify

= 6 x - 6 y

\frac{d}{d x} (arcsin (\frac{2 x}{1 + x ^{2}}))

\frac{d}{d t} (- 3 e^{- 3 t})

4 sin (x + \frac{π}{3}) - 1

\frac{\partial}{\partial y} (1 + 2 x y)

What is (\partial)/(\partial x)(3x^2-6xy+y^3-9y+5) ?
The answer to (\partial)/(\partial x)(3x^2-6xy+y^3-9y+5) is 6x-6y